Computational Structural Concrete
Theory and Applications
2. Edition October 2022
XVIII, 424 Pages, Softcover
161 Pictures
11 tables
Handbook/Reference Book
Short Description
Basic concepts of numerical methods, in particular the FEM are summarized. The theory is explicated for structural concrete parts like beams, plates, slabs and shells and illustrated by 42 examples. Thus, the operation of complex software is made transparent. (incl. ebook as PDF)
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Concrete is by far the most used building material due to its advantages: it is shapeable, cost-effective and available everywhere. Combined with reinforcement it provides an immense bandwidth of properties and may be customized for a huge range of purposes. Thus, concrete is the building material of the 20th century. To be the building material of the 21th century its sustainability has to move into focus. Reinforced concrete structures have to be designed expending less material whereby their load carrying potential has to be fully utilized.
Computational methods such as Finite Element Method (FEM) provide essential tools to reach the goal. In combination with experimental validation, they enable a deeper understanding of load carrying mechanisms. A more realistic estimation of ultimate and serviceability limit states can be reached compared to traditional approaches. This allows for a significantly improved utilization of construction materials and a broader horizon for innovative structural designs opens up.
However, sophisticated computational methods are usually provided as black boxes. Data is fed in, the output is accepted as it is, but an understanding of the steps in between is often rudimentary. This has the risk of misinterpretations, not to say invalid results compared to initial problem definitions. The risk is in particular high for nonlinear problems. As a composite material, reinforced concrete exhibits nonlinear behaviour in its limit states, caused by interaction of concrete and reinforcement via bond and the nonlinear properties of the components. Its cracking is a regular behaviour. The book aims to make the mechanisms of reinforced concrete transparent from the perspective of numerical methods. In this way, black boxes should also become transparent.
Appropriate methods are described for beams, plates, slabs and shells regarding quasi-statics and dynamics. Concrete creeping, temperature effects, prestressing, large displacements are treated as examples. State of the art concrete material models are presented. Both the opportunities and the pitfalls of numerical methods are shown. Theory is illustrated by a variety of examples. Most of them are performed with the ConFem software package implemented in Python and available under open-source conditions.
(incl. ebook as PDF)
List of Examples*
Notation
1 INTRODUCTION
2 FINITE ELEMENTS OVERVIEW
2.1 Modelling Basics
2.2 Discretisation Outline
2.3 Elements
2.4 Material Behavior
2.5 Weak Equilibrium
2.6 Spatial Discretisation
2.7 Numerical Integration
2.8 Equation Solution Methods
2.9 Discretisation Errors
3 UNIAXIAL REINFORCED CONCRETE BEHAVIOUR
3.1 Uniaxial Stress-Strain Behaviour of Concrete
3.2 Long-Term Behaviour - Creep and Imposed Strains
3.3 Reinforcing Steel Stress-Strain Behaviour
3.4 Bond between Concrete and Reinforcement
3.5 Smeared Crack Model
3.6 Reinforced Tension Bar
3.7 Tension Stiffening of Reinforced Bars
4 STRUCTURAL BEAMS AND FRAMES
4.1 Cross-Sectional Behaviour
4.2 Equilibrium of Beams
4.3 Finite Elements for Plane Beams
4.4 System Building and Solution
4.5 Creep of Concrete
4.6 Temperature and Shrinkage
4.7 Tension Stiffening
4.8 Prestressing
4.9 Large Displacements - Second-Order Analysis
4.10 Dynamics
5 STRUT-AND-TIE MODELS
5.1 Elastic Plate Solutions
5.2 Strut-and-Tie Modelling
5.3 Solution Methods for Trusses
5.4 Rigid Plastic Truss Models
5.5 Application Aspects
6 MULTI-AXIAL CONCRETE BEHAVIOUR
6.1 Basics
6.2 Continuum Mechanics
6.3 Isotropy, Linearity, and Orthotropy
6.4 Nonlinear Material Behaviour
6.5 Elasto-Plasticity
6.6 Damage
6.7 Damaged Elasto-Plasticity
6.8 The Microplane Model
6.9 General Requirements for Material Laws
7 CRACK MODELLING AND REGULARISATION
7.1 Basic Concepts of Crack Modelling
7.2 Mesh Dependency
7.3 Regularisation
7.4 Multi-Axial Smeared Crack Model
7.5 Gradient Methods
7.6 Overview of Discrete Crack Modelling
7.7 The Strong Discontinuity Approach
8 PLATES
8.1 Lower Bound Limit State Analysis
8.2 Cracked Concrete Modelling
8.3 Reinforcement and Bond
8.4 Integrated Reinforcement
8.5 Embedded Reinforcement with a Flexible Bond
9 SLABS
9.1 Classification
9.2 Cross-Sectional Behaviour
9.3 Equilibrium of Slabs
9.4 Reinforced Concrete Cross-Sections
9.5 Slab Elements
9.6 System Building and Solution Methods
9.7 Lower Bound Limit State Analysis
9.8 Nonlinear Kirchhoff Slabs
9.9 Upper Bound Limit State Analysis
10 SHELLS
10.1 Geometry and Displacements
10.2 Deformations
10.3 Shell Stresses and Material Laws
10.4 System Building
10.5 Slabs and Beams as a Special Case
10.6 Locking
10.7 Reinforced Concrete Shells
11 RANDOMNESS AND RELIABILITY
11.1 Uncertainty and Randomness
11.2 Failure Probability
11.3 Design and Safety Factors
12 CONCLUDING REMARKS
APPENDIX A SOLUTION METHODS
A.1 Nonlinear Algebraic Equations
A.2 Transient Analysis
A.3 Stiffness for Linear Concrete Compression
A.4 The Arc Length Method
APPENDIX B MATERIAL STABILITY
APPENDIX C CRACK WIDTH ESTIMATION
APPENDIX D TRANSFORMATIONS OF COORDINATE SYSTEMS
APPENDIX E REGRESSION ANALYSIS
References
Index
*LIST OF EXAMPLES
3.1 Tension bar with localisation
3.2 Tension bar with creep and imposed strains
3.3 Simple uniaxial smeared crack model
3.4 Reinforced concrete tension bar
4.1 Moment-curvature relations for given normal forces
4.2 Simple reinforced concrete (RC) beam
4.3 Creep deformations of RC beam
4.4 Effect of temperature actions on an RC beam
4.5 Effect of tension stiffening on an RC beam with external and temperature loading
4.6 Prestressed RC beam
4.7 Stability limit of cantilever column
4.8 Ultimate limit for RC cantilever column
4.9 Beam under impact load
5.1 Continuous interpolation of stress fields with the quad element
5.2 Deep beam with strut-and-tie model
5.3 Corbel with an elasto-plastic strut-and-tie model
6.1 Mises elasto-plasticity for uniaxial behavior
6.2 Uniaxial stress-strain relations with Hsieh-Ting-Chen damage
6.3 Stability of Hsieh-Ting-Chen uniaxial damage
6.4 Microplane uniaxial stress-strain relations with de Vree damage
7.1 Plain concrete plate with notch
7.2 Plain concrete plate with notch and crack band regularisation
7.3 2D smeared crack model with elasticity
7.4 Gradient damage formulation for the uniaxial tension bar
7.5 Phase field formulation for the uniaxial tension bar
7.6 Plain concrete plate with notch and SDA crack modeling
8.1 Reinforcement design for a deep beam with a limit state analysis
8.2 Simulation of cracked reinforced deep beam
8.3 Simulation of a single fibre connecting a dissected continuum
8.4 Reinforced concrete plate with flexible bond
9.1 Linear elastic slab with opening and free edges
9.2 Reinforcement design for a slab with opening and free edges with a limit state analysis
9.3 Computation of shear forces and shear design
9.4 Elasto-plastic slab with opening and free edges
9.5 Simple RC slab under concentrated loading
9.6 Simple RC slab with yield line method and distributed loading
9.7 Simple RC slab with yield line method and concentrated loading
10.1 Convergence study for linear simple slab
10.2 Simple RC slab with interaction of normal forces and bending
11.1 Analytical failure probability of cantilever column
11.2 Approximate failure probability of cantilever column with Monte Carlo integration
11.3 Simple partial safety factor derivation
